It's quite difficult for this match, but I'm sure Arsenal will win at home.
Arteta at the beginning of the season did such a difficult task, Aston Villa has been defeated, now Brighton will be difficult but I think Arsenal are able to beat them, for the week's match with Spurs I think Arsenal will be quite difficult as away.
I agree with you that Arsenal will be the winner at their home stadium but Brighton are strong enough to challenge Arsenal in this match. Arteta will need to lead Arsenal in Premier League to have as many points as possible, and use it as chances to strengthen his team and prepare for matches in Champions League too. I believe Arteta and Arsenal will prioritize Premier League but they will also try in Champions League. Because going far in Champions League means more money for their club, that can be used to buy one or two more players next summer transfer season.
The match has been going on for 20 minutes, but the score is still 0-0. Arsenal appeared more dominant and they also had more chances, but Brighton could defend quite well so far. Actually, there was a good chance that Odengard had in the box but unfortunately, he couldn't shoot well enough. This is really not an easy match, but I think Arsenal will still come out as winners.